This is a problem of compound interest with monthly deposits. The formula to calculate the future value of an account with regular monthly deposits is given by the future value of an annuity formula:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

Where:

• $FV$ is the future value of the account.
• $P$ is the amount deposited each period ($425).
• $r$ is the monthly interest rate (APR divided by 12).
• $n$ is the total number of deposits (monthly deposits for 31 years).

Step-by-Step Solution:

1. Annual interest rate (APR): 10.6% or 0.106.

   • The monthly interest rate is $r = \frac{0.106}{12} = 0.0088333$.

2. Number of periods (n): Since the deposits are made monthly for 31 years: $n = 31 \times 12 = 372$

3. Substitute the values into the formula: $FV = 425 \times \frac{(1 + 0.0088333)^{372} - 1}{0.0088333}$

Let's calculate this:

$FV = 425 \times \frac{(1.0088333)^{372} - 1}{0.0088333}$

Now, let's compute this using the exact values. Given values P = 425 # monthly deposit r = 0.106 / 12 # monthly interest rate n = 31 * 12 # total number of periods (months)

Future value formula for monthly deposits

FV = P * ((1 + r)**n - 1) / r FVThe future value of your retirement account after 31 years, with monthly deposits of $425 and an APR of 10.6% compounded monthly, will be $1,219,800.99.

Let me know if you would like any further explanation or have additional questions!

Here are some related questions for you:

1. How would the future value change if the monthly deposit amount was increased to $500?
2. What would the future value be if the interest rate were 8% instead of 10.6%?
3. How much would you need to deposit monthly to reach a retirement account of $2,000,000 in 31 years with the same interest rate?
4. What is the total amount deposited over the 31 years, and how does it compare to the future value?
5. How would the future value differ if the deposits were made annually instead of monthly?

Tip: When calculating compound interest with regular deposits, it's important to ensure that both the interest rate and the number of periods align (i.e., both are based on the same time frame).